On a certain sum of money lent out at 16% per annum, the difference between the compound interest for 1 year, payable half-yearly, and the simple interest for 1 year is Rs. 60. The sum is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. Rs. 9375
Given that
[(C.I.)half yearly for 1 year] - [S.I. for 1 year] = Rs. 60
Rate of interest = 16% p.a.
Formula used
C.I. = P(1 + Rate/100)time - P
S.I. = PRT/100
where, P is sum, R = rate of interest, T = time, C.I. = compound interest, and S.I = simple interest
Calculation
For half yearly
Rate of interest = 16/2 = 8%
Time = 2 × 1 = 2 years
(C.I.)half yearly = P (1 + 8/100)2 - P =P (27/25)2 - P = 729P/625 - P = 104P/625
S.I. = P × 16 × 1/100 = 0.16P
Now,
⇒ 104P/625 - 0.16P = Rs. 60
⇒ 0.1664P - 0.16P = Rs. 60
⇒ P = 60/0.0064 = Rs. 9375